Maths with letters!

12, 6, 2, 3.14, 22,317, -6, 123 Constants (Don’t Change) x, y, z, a, b, c Variables (Unknown Numbers)

Order of Operations B O M D A S

3 X a = 3a 4 X 5 X y = 20y 2 X a X 3 X b = 2 X 3 X a X b = 6ab a X b = ab 5 X 6y = 30y 2 X 3xy X 5z = (2)(3)(5)xyz = 30xyz Multiplying 1

Substitution 1 If x = 3 and y = 4, find the value of 4x + y 4(3) xy (3)(4) 12 3x – 2y 3(3) – 2(4) xy- 2y 3(3)(4) – 2(4) 36 – x – 3y + 5 6(3) – 3(4) –

Adding and Subtracting Integers

Adding and Subtracting Integers Same signs add and keep, Different signs subtract, Keep the sign of the higher number, Then it’ll be exact, = = = – 6 = = = 7

Adding Like Terms Look for the Like Terms Rewrite with the Like Terms Together Add and Subtract the Like Terms 2a+ 4xy+ 7– 9xy+ 3a– 3– a 2a+ 4xy+ 7– 9xy+ 3a– 3– a 4a– 5xy + 4

Adding Like Terms (i) 3x x -2 = 3x + 5x = 8x + 2 (ii) 3a + 4b –a + 2b + 2a = 3a –a + 2a + 4b + 2b = 4a + 6b

Adding Like Terms 3x x – 2 3x + 5x + 4 – 2 8x +2 3a + 4b –a – 7b + 2a 3a – a + 2a + 4b – 7b 4a – 3b 2ab + c + 5ab + 2c 2ab + 5ab + c + 2c 7ab + 3c 4xy + 2x + 4x - 8xy – x 4xy – 8xy + 2x + 4x – x – 4xy + 5x

Multiplying + - Like Signs Give Plus Unlike Signs Give Minus 3 X 4 = 12 6 X – 2 = – 12 – 2 X – 4 = 8 – 3(3x) = – 9x – 5 X 3 = – 15 a) 5 X 5 = d) – 4 X – 3 = b) – 5 X – 2 = e) 3 X – 7 = c) – 3 X 2 = f) – 4 X – 6 = g) 3(2x) =h) 3(–2x) =i) –3(–2x) j) – 3(2x) =k) – 3(2x + 6) = l) –3(2x – 6) – 3(– 4x) = 12x

Removing Brackets 4 (3 + 2) 3 (x + 2) 5(2a + 3b) 2(x+4) + 3(2x +6) 2(3x +2y – 4) – 2(2y – 4) x+ 6 10a+15b 2x+8+6x+18 2x+8+6x+18 8x+26 6x+4y– 8 – 4y+ 8

Indices 2 = 2 X 2 = = 3 X 3 = = 2 X 2 X 2 = = 4 X 4 X 4 = 64 a2a2 = a X a b3b3 = b X b X b 5252 = 5 X 5 = = 5 X 5 X 5 X 5 = 625 y4y4 = y X y X y X y y X y = y 2 a X a = a 2 2a X 3a = 6a 2

Removing Brackets x(x + 2) 2x(x + 4) 3x(2x – 9) 2x(x+4) + 5x(3x – 2) x2x2 + 2x 2x 2 + 8x 6x 2 – 27x 2x 2 +8x+15x 2 – 10x 2x 2 +8x+15x 2 – 10x 17x 2 – 2x – a(a+3) + 3a(5a – 2) – a 2 – 3a+15a 2 – 6a – a 2 – 3a+15a 2 – 6a 14a 2 – 9a b(b – 3) – 3b(– 5b – 2) b2b2 – 3b+15b 2 + 6b b2b2 – 3b+15b 2 + 6b 16b 2 + 3b

Substitution 2 If x = 3 and y = 4, find the value of x2x X 3 9 2x 2 – 2y 2(3 2 ) – 2(4) 2( 3 X 3) – 8 2 (9) – 8 = 10 6x – 3y + 5 6(3) – 3(4) – y2y X x 2 – 2y 2(3 2 ) – 2(4) 2( 3 X 3) – 8 2 (9) – 8 = 10

Removing More Brackets! x+2 x2x2 +3x+2x+6 x2x2 +5x+6 (x + 2) (x + 3) 2x– 5 2x 2 +6x– 5x–15 2x 2 +x– 15 (2x – 5) (x + 3) 4x+ 4 8x 2 – 12x+ 8x–12 8x 2 – 4x– 12 (4x + 4) (2x – 3) x +2 x2x2 +3x+xy+2x x2x2 +3x+6 (x + 2) (x y) +6+2y +2x+xy+2y x2x2 +5x+6+xy+2y

Simplify Multiply Out the Brackets Add and Subtract the Like Terms 2(x+4) + 5(x -2) 2x+ 8+ 5x– 10 2x+ 8– 10+ 5x 7x– 2